In addition to reanalysis, panels (a,b) also display a small sample of the S2S dataset in purple. These are not forecasts but reforecasts, or hindcasts, generated by initializing a present-day model version on past weather conditions. The S2S archive compiles forecasts and hindcasts from 11 forecasting centers around the world [1]}, with a principle goal of tracking improvements in skill from one version to the next. In this study we restrict ourselves to the ECMWF IFS, although our methodology can be repeated on other S2S datasets for intercomparison. We use data from the 2017 model version CY43R1, which produced 21 full winters of hindcasts between autumn of 1996 and spring of 2017. These are initialized using ERA-Interim (ERA-I) reanalysis [2]}, which is is almost identical to the more advanced ERA-5 from the standpoint of \(U_{10,60}\) . Two ensembles are launched every week, each with eleven members (one control and ten perturbed forecasts) that run for 47 days before terminating. We use only the ten perturbed members, which are initialized using a singular vector method and integrated with stochastic physics schemes [3]}. This introduces randomness into the ensemble, causing the members to drift apart over time after the initialization date, as shown in Fig. REF (c,d) for two sample ensembles. The specific strategy for perturbation of initial conditions and stochastic physics is informed by chaotic dynamical systems theory and has been refined by decades of numerical experiments [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]} aimed at reducing forecast error due to under-dispersion, especially in the face of oncoming flow regime transitions [12]}. In total, the S2S dataset contains over 900 years of simulation time. Many of them reach farther into the negative-\(U_{10,60}\)  tails than reanalysis, allowing us to calculate otherwise inaccessible probabilities.
